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Integration of Immune Cell-Target Cell Conjugate Dynamics Changes the Time Scale of Immune Control of Cancer. [PDF]

Bull Math Biol
Yang Q, Traulsen A, Altrock PM.
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Stochastic Differential Equations

2014
Stochastic differential equations describe the time evolution of certain continuous n-dimensional Markov processes. In contrast with classical differential equations, in addition to the derivative of the function, there is a term that describes the random fluctuations that are coded as an Ito integral with respect to a Brownian motion. Depending on how
Etienne Pardoux, Aurel Răşcanu
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Stochastic Differential Equations [PDF]

, 1990
A diffusion can be thought of as a strong Markov process (in ℝn) with continuous paths. Before the development of Ito’s theory of stochastic integration for Brownian motion, the primary method of studying diffusions was to study their transition semigroups.
R. J. Williams, K. L. Chung
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Stochastic Differential Equations

2012
This chapter represents the core of the book. Building on the general theory introduced in previous chapters, stochastic differential equations (SDEs) are presented as a key mathematical tool for relating the subject of dynamical systems to Wiener noise.
Vincenzo Capasso, David Bakstein
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Stochastic Differential Equations [PDF]

, 1988
We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of ...
Steven E. Shreve, Ioannis Karatzas
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Stochastic differential equations

Physics Reports, 1976
Abstract In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ c , where α measures the size of the fluctuations and τ c their autocorrelation time. This
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Stochastic Differential Equations

2009
The chapter begins with Section 4.1 in which motivational examples of random walks and stochastic phenomena in nature are presented. In Section 4.2 the concept of random processes is introduced in a more precise way. In Section 4.3 the concept of a Gaussian and Markov random process is developed. In Section 4.4 the important special case of white noise
Alexander Kukush, Andrey Pilipenko, Dmytro Gusak, Alexey Kulik, Yuliya Mishura   +4 more
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Stochastic Differential Equations

2019
In this chapter, we consider the stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion. The conditions and proofs of existence and uniqueness of a stochastic differential equation is similar to the classical situation.
Radek Erban, S. Jonathan Chapman
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Stochastic Differential Equations

1991
In previous chapters stochastic differential equations have been mentioned several times in an informal manner. For instance, if M is a continuous local martingale, its exponential e(M) satisfies the equality $$\mathcal{E}{(M)_t} = 1 + \int_0^t {\mathcal{E}{{(M)}_s}} d{M_s};$$ this can be stated: e(M) is a solution to the stochastic differential
Daniel Revuz, Marc Yor
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Stochastic differential equations

2011
In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.
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