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# Questions tagged [stochastic-processes]

A stochastic process is a collection of random variables usually indexed by a totally ordered set.

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### Conditioning on future events, strong Markov property, independence

I have a question on an argument appearing in this article P. Setting Let $S=(1,\infty) \times (-1,1) \subset \mathbb{R}^2$ and let $X=(\{X_t\},\{P_x\}_{x \in S})$ be a diffusion process on $S$. ...
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### Inequalities for moments of a certain integral

Let $X(t)$ be a stationary Gaussian process, $EX(t)=0$, the correlation function $R(\tau)$ is given. What bounds from above can be given for the $p$-th moment ($p>0, p \in \mathbb{R}$) of the ...
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### Random Two-Player Asymmetric Game

About half a year ago I asked a question on MSE about a random two player game. At the time, the question received some attention and some progress was made, but was not resolved completely. I have ...
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### Distribution Functions in Poisson Process

We consider definition of Poisson processes that satisfy Condition 0 and 1 according to Billingsley section 23 . How find out the densities of $A_t , B_t , L_t$ defined as in problems section of ...
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### A modification of Kolmogorov's continuity criterion for $C_{tem}$

I am wondering about how to prove a modification of Kolmogrov's continuity criterion in order to also being able to quantify the growth behaviour of the process. In particular, I am interested in the ...
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Suppose that $X$ is the continuous-time simple symmetric random walk on the lattice $\mathbb Z^d$ (i.e., a simple symmetric random walk with i.i.d. exponential jump times), and let $$u(t,x):=\mathbf E\... 1answer 190 views ### Obtaining generator matrix and first-passage time distribution for CTMC? Setup: I have a model of a biological process described by two ODEs as follows:$$\dot{X_1} = (\beta_1-d-1)X_1 + 2X_1^2 - X_1^3 + dX_2\dot{X_2} = (\beta_2-d-1)X_2 + 2X_2^2 - X_2^3 + dX_1 I ...

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