Existence uniqueness of mild solutions for ψ-Caputo fractional stochastic evolution equations driven by fBm

In this paper, we investigate the existence uniqueness of mild solutions for a class of ψ-Caputo fractional stochastic evolution equations with varying-time delay driven by fBm, which seems to be the first theoretical result of the ψ-Caputo fractional stochastic evolution equations. Alternative conditions to guarantee the existence uniqueness of mild solutions are obtained using fractional calculus, stochastic analysis, fixed point technique, and noncompact measure method. Moreover, an example is presented to illustrate the effectiveness and feasibility of the obtained abstract results.

Weak pullback mean random attractors for stochastic evolution equations and applications

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction–diffusion equations, the stochastic [Formula: see text]-Laplace equation and stochastic porous media equations are established.

Solving Schrödinger Bridges via Maximum Likelihood

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.

A scenario-based interval-input output model to analyze the risk of COVID-19 pandemic in port logistics

Purpose Presently, Indian sectors are manifesting a higher level of interdependency and making the economy more vulnerable to human-caused and natural disasters. COVID-19 pandemic creates a devastating effect on the world economy. The Indian economy was expected to lose around ₹ 32,000 crores every day during the first 21 days of complete lockdown. This motivates to conduct the research on how the COVID-19 pandemic affects the port logistics sector and how the effects of COVID-19 on port logistics propagate to other sectors owing to its interconnectedness and affect the economy of the country. Design/methodology/approach The purpose of the study is analyze how perturbation in one sector can affect the system of interdependent sectors and it is done with interdependency analysis. It uses Wassily Leontief’s inoperability input-output model (IIM) and interval programming (IP) to develop a framework. IP is used to address situations where assumptions are not valid because of uncertainties associated with disruptive events. Findings The model helps in describing how the effect of the COVID-19 pandemic in port logistics can propagate owing to the interconnectedness across other sectors. The model uses the latest five-year data available on the Organisation for Economic Co-operation and Development database. It uses metrics like inoperability and economic loss to study the consequences of COVID-19 pandemic on various sectors. This study also presents the ranking of the affected sectors based on their inoperability and economic loss Research limitations/implications In the future study, other techniques like dynamic evolution, multiplex network analysis, analytical hierarchy process, pinch analysis, stochastic evolution and pinch graph could be integrated with input-output (I-O) modelling. Integrated stochastic evolution with an I-O model allows capturing the likelihood of the events; it includes probability distributions instead of point estimates for scenario parameters. Methods like dynamic evolution and multiplex network analysis can be introduced in future work to shed lights on interdependency among the sector, which could potentially provide additional insights for transport policy formulations. Originality/value This study discusses the theory, methodology and application of the IIM-IP model in the domain of port logistics. The developed IIM-IP model helps decision-makers to manage risk in port logistics. Firstly, it studies how different sectors are interconnected with each other. Secondly, it helps in identifying the most vulnerable sectors based on economic loss and inoperability. Thirdly, it provides the ranking of the sectors based on their economic losses.