scholarly journals A Continuation Principle for Periodic BV-Continuous State-Dependent Sweeping Processes

2020 ◽  
Vol 52 (6) ◽  
pp. 5598-5626
Author(s):  
Mikhail Kamenskii ◽  
Oleg Makarenkov ◽  
Lakmi N. Wadippuli
Keyword(s):  
Continuation Principle ◽  
State Dependent ◽  
Continuous State ◽  
Sweeping Processes

The virtual waiting-time and related processes

1986 ◽  
Vol 18 (02) ◽  
pp. 558-573 ◽  
Author(s):  
D. R. Cox ◽  
Valerie Isham
Keyword(s):  
Waiting Time ◽  
Arrival Rate ◽  
Transient Behaviour ◽  
Decay Properties ◽  
State Dependent ◽  
Continuous State Space ◽  
Virtual Waiting Time ◽  
Continuous State ◽  
Waiting Time Process ◽  
Properties Of Soil

The virtual waiting-time process of Takács is one of the simplest examples of a stochastic process with a continuous state space in continuous time in which jump transitions interrupt periods of deterministic decay. Properties of the process are reviewed, and the transient behaviour examined in detail. Several generalizations of the process are studied. These include two-sided jumps, periodically varying ‘arrival’ rate and the presence of a state-dependent decay rate; the last case is motivated by the properties of soil moisture in hydrology. Throughout, the emphasis is on the derivation of simple interpretable results.

scholarly journals Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

2009 ◽  
Vol 46 (1) ◽  
pp. 221-243 ◽  
Author(s):  
Fubao Xi ◽  
G. Yin
Keyword(s):  
Field Model ◽  
Asymptotic Properties ◽  
Mean Field ◽  
Switching Process ◽  
Mean Field Model ◽  
State Dependent ◽  
Uniform Ergodicity ◽  
Continuous State ◽  
Feller Continuity ◽  
Drift Conditions

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

scholarly journals Learning Probabilistic Termination Proofs

2021 ◽  
pp. 3-26
Author(s):  
Alessandro Abate ◽  
Mirco Giacobbe ◽  
Diptarko Roy
Keyword(s):  
Learning Strategy ◽  
Source Code ◽  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
Execution Traces ◽  
State Dependent ◽  
Polynomial Programs ◽  
Continuous State ◽  
Guided Inductive ◽  
Probabilistic Programs

AbstractWe present the first machine learning approach to the termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that probabilistic programs halt, in expectation, within a finite number of steps. While previously RSMs were directly synthesised from source code, our method learns them from sampled execution traces. We introduce the neural ranking supermartingale: we let a neural network fit an RSM over execution traces and then we verify it over the source code using satisfiability modulo theories (SMT); if the latter step produces a counterexample, we generate from it new sample traces and repeat learning in a counterexample-guided inductive synthesis loop, until the SMT solver confirms the validity of the RSM. The result is thus a sound witness of probabilistic termination. Our learning strategy is agnostic to the source code and its verification counterpart supports the widest range of probabilistic single-loop programs that any existing tool can handle to date. We demonstrate the efficacy of our method over a range of benchmarks that include linear and polynomial programs with discrete, continuous, state-dependent, multi-variate, hierarchical distributions, and distributions with undefined moments.

scholarly journals Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

2009 ◽  
Vol 46 (01) ◽  
pp. 221-243
Author(s):  
Fubao Xi ◽  
G. Yin
Keyword(s):  
Field Model ◽  
Asymptotic Properties ◽  
Mean Field ◽  
Switching Process ◽  
Mean Field Model ◽  
State Dependent ◽  
Uniform Ergodicity ◽  
Continuous State ◽  
Feller Continuity ◽  
Drift Conditions

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

Sign in / Sign up

Export Citation Format

Share Document