arXiv subjects

Pingjin Deng

Publications and source records attributed to Pingjin Deng.

3 recordsLinked to original sources

arXiv2016

Asymptotic of Non-Crossings probability of Additive Wiener Fields

Let $W_i=\{W_i(t_i), t_i\in \R_+\}, i=1,2,\ldots,d$ are independent Wiener processes. $W=\{W(\mathbf{t}),t\in \R_+^d\}$ be the additive Wiener field define as the sum of $W_i$. For any trend $f$ in $\kHC$ (the reproducing kernel Hilbert Space of $W$), we derive upper and lower bounds for the boundary non-crossing probability $$P_f=P\{\sum_{i=1}^{d}W_i(t_i) +f(\mathbf{t})\leq u(\mathbf{t}), \mathbf{t}\in\R_+^d\},$$ where $u: \R_+^d\rightarrow \R_+$ is a measurable function. Furthermore, for large trend functions $γf>0$, we show that the asymptotically relation $\ln P_{γf}\sim \ln P_{γ\underline{f}}$ as $γ\to \IF$, where $\underline{f}$ is the projection of $f$ on some closed convex subset of $\kHC$.

math.PR↗

arXiv2016

The joint distributions of running maximum of a Slepian processes

Consider the Slepian process $S$ defined by $ S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain and the maximum $M_t=\max_{0\leq u\leq t}S(u)$ for $0< s < t$ fixed. Explicit integral expression are obtained for the distribution function of the partial maximum $m_{s}$ and the joint distribution function between $m_{s}$ and $M_t$. We also use our results to determine the moments of $m_{s}$.

math.PR↗

arXiv2016

The boundary non-Crossing probabilities for Slepian process

In this contribution we derive an explicit formula for the boundary non-crossing probabilities for Slepian processes associated with the piecewise linear boundary function. This formula is used to develop an approximation formula to the boundary non-crossing probabilities for general continuous boundaries. The formulas we developed are easy to implement in calculation the boundary non-crossing probabilities.

math.PR↗