• Title, Summary, Keyword: Stochastic diffusion

Search Result 56, Processing Time 0.093 seconds

EULER-MARUYAMA METHOD FOR SOME NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMP-DIFFUSION

  • Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.18 no.1
    • /
    • pp.43-50
    • /
    • 2014
  • In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.

EXISTENCE OF RANDOM ATTRACTORS FOR STOCHASTIC NON-AUTONOMOUS REACTION-DIFFUSION EQUATION WITH MULTIPLICATIVE NOISE ON ℝn

  • Mosa, Fadlallah Mustafa;Ma, Qiaozhen;Bakhet, Mohamed Y.A.
    • Korean Journal of Mathematics
    • /
    • v.26 no.4
    • /
    • pp.583-599
    • /
    • 2018
  • In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

ON STOCHASTIC EVOLUTION EQUATIONS WITH STATE-DEPENDENT DIFFUSION TERMS

  • Kim, Jai-Heui;Song, Jung-Hoon
    • Journal of the Korean Mathematical Society
    • /
    • v.34 no.4
    • /
    • pp.1019-1028
    • /
    • 1997
  • The integral solution for a deterministic evolution equation was introduced by Benilan. Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic evolution euation under some conditions for the coefficients. Moreover we prove that this solution is a unique strong solution.

  • PDF

A combined stochastic diffusion and mean-field model for grain growth

  • Zheng, Y.G.;Zhang, H.W.;Chen, Z.
    • Interaction and multiscale mechanics
    • /
    • v.1 no.3
    • /
    • pp.369-379
    • /
    • 2008
  • A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

THE APPLICATION OF STOCHASTIC ANALYSIS TO COUNTABLE ALLELIC DIFFUSION MODEL

  • Choi, Won
    • Bulletin of the Korean Mathematical Society
    • /
    • v.41 no.2
    • /
    • pp.337-345
    • /
    • 2004
  • In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

Bayesian Inference of the Stochastic Gompertz Growth Model for Tumor Growth

  • Paek, Jayeong;Choi, Ilsu
    • Communications for Statistical Applications and Methods
    • /
    • v.21 no.6
    • /
    • pp.521-528
    • /
    • 2014
  • A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS

  • KIM JAI HEUI
    • Journal of the Korean Mathematical Society
    • /
    • v.42 no.1
    • /
    • pp.153-169
    • /
    • 2005
  • A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

STOCHASTIC MOLECULAR DYNAMICS SIMULATION OF PARTICLE DIFFUSION IN RECTANGULAR MICROCHANNELS (스토캐스틱 분자동역학 시뮬레이션을 통한 직사각형 마이크로 채널 내의 입자 확산 연구)

  • Kim, Yong-Rok;Park, Chul-Woo;Kim, Dae-Joong
    • 한국전산유체공학회:학술대회논문집
    • /
    • /
    • pp.204-207
    • /
    • 2008
  • Stochastic molecular dynamics simulation is a variation of standard molecular dynamics simulation that basically omits water molecules. The omission of water molecules, occupying a majority of space, enables flow simulation at microscale. This study reports our stochastic molecular dynamics simulation of particles diffusing in rectangular microchannels. We interestingly found that diffusion patterns in channels with a very small aspect ratio differ by dimensions. We will also discuss the future direction of our research toward a more realistic simulation of micromixing.

  • PDF

STOCHASTIC MOLECULAR DYNAMICS SIMULATION OF PARTICLE DIFFUSION IN RECTANGULAR MICROCHANNELS (스토캐스틱 분자동역학 시뮬레이션을 통한 직사각형 마이크로 채널 내의 입자 확산 연구)

  • Kim, Yong-Rok;Park, Chul-Woo;Kim, Dae-Joong
    • 한국전산유체공학회:학술대회논문집
    • /
    • /
    • pp.204-207
    • /
    • 2008
  • Stochastic molecular dynamics simulation is a variation of standard molecular dynamics simulation that basically omits water molecules. The omission of water molecules, occupying a majority of space, enables flow simulation at microscale. This study reports our stochastic molecular dynamics simulation of particles diffusing in rectangular microchannels. We interestingly found that diffusion patterns in channels with a very small aspect ratio differ by dimensions. We will also discuss the future direction of our research toward a more realistic simulation of micromixing.

  • PDF

THE APPLICATION OF STOCHASTIC DIFFERENTIAL EQUATIONS TO POPULATION GENETIC MODEL

  • Choi, Won;Choi, Dug-Hwan
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.4
    • /
    • pp.677-683
    • /
    • 2003
  • In multi-allelic model $X\;=\;(x_1,\;x_2,\;\cdots\;,\;x_d),\;M_f(t)\;=\;f(p(t))\;-\;{\int_0}^t\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we examine the stochastic differential equation for model X and find the properties using stochastic differential equation.