Related papers: Extreme hitting probabilities for diffusion
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
A one-dimensional, continuous, regular, and strong Markov process $X$ with state space $E$ hits any point $z \in E$ fast with positive probability. To wit, if $\tau_z = \inf \{t \geq 0:X_{t} = z\}$, then $P_\xi({ \tau}_z<\varepsilon)>0$ for…
We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
The Estimation of Distribution Algorithm is a new class of population based search methods in that a probabilistic model of individuals is estimated based on the high quality individuals and used to generate the new individuals. In this…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
The uniformly optimal search plan is a cornerstone of the optimal search theory. It is well-known that when the target distribution is circular normal and the detection function is exponential, the uniformly search plan has several…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
Consider a two-person zero-sum search game between a Hider and a Searcher. The Hider chooses to hide in one of $n$ discrete locations (or "boxes") and the Searcher chooses a search sequence specifying which order to look in these boxes…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
We consider two independent identical diffusion processes that annihilate upon meeting in order to study their conditioning with respect to their first-encounter properties. For the case of finite horizon $T<+\infty$, the maximum…
The probability that a max-stable process {\eta} in C[0, 1] with identical marginal distribution function F hits x \in R with 0 < F (x) < 1 is the hitting probability of x. We show that the hitting probability is always positive, unless the…
By considering any one-dimensional time-homogeneous solvable diffusion process,this paper develops a complete analytical framework for computing the distribution of the last hitting time, to any level, and its joint distribution with the…
Diffusion models have shown promising generative capabilities across diverse domains, yet aligning their outputs with desired reward functions remains a challenge, particularly in cases where reward functions are non-differentiable. Some…
This paper investigates a partial-information pursuit evasion game in which the Pursuer has a limited-range sensor to detect the Evader. Given a fixed final time, we derive the optimal evasion strategy for the Evader to maximize its…
We present a dynamic programming-based solution to the problem of maximizing the probability of attaining a target set before hitting a cemetery set for a discrete-time Markov control process. Under mild hypotheses we establish that there…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…