The-Square-and-Add Markov Chain
نویسندگان
چکیده
Squaring and adding $\pm 1$ mod p generates a curiously intractable random walk. A similar process over the finite field $\mathbf{F}_q$ (with $q=2^d$) leads to novel connections between elementary Galois theory probability.
منابع مشابه
Relative Entropy Rate between a Markov Chain and Its Corresponding Hidden Markov Chain
In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...
متن کاملanalysis of ruin probability for insurance companies using markov chain
در این پایان نامه نشان داده ایم که چگونه می توان مدل ریسک بیمه ای اسپیرر اندرسون را به کمک زنجیره های مارکوف تعریف کرد. سپس به کمک روش های آنالیز ماتریسی احتمال برشکستگی ، میزان مازاد در هنگام برشکستگی و میزان کسری بودجه در زمان وقوع برشکستگی را محاسبه کرده ایم. هدف ما در این پایان نامه بسیار محاسباتی و کاربردی تر از روش های است که در گذشته برای محاسبه این احتمال ارائه شده است. در ابتدا ما نشا...
15 صفحه اولThe Markov chain market
We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differ...
متن کاملMarkov Chain and Hidden Markov Model
Figure 1. Finite state machine for a Markov chain X0 → X1 → X2 → · · · → Xn where the random variables Xi’s take values from I = {S1, S2, S3}. The numbers T (i, j)’s on the arrows are the transition probabilities such that Tij = P (Xt+1 = Sj|Xt = Si). Definition 1.2. We say that (Xn)n≥0 is a Markov chain with initial distribution λ and transition matrix T if (i) X0 has distribution λ; (ii) for ...
متن کاملregression analysis in markov chain
in a finite stationary markov chain, transition probabilities may depend on some explanatoryvariables. a similar problem has been considered here. the corresponding posteriors are derived andinferences are done using these posteriors. finally, the procedure is illustrated with a real example.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Mathematical Intelligencer
سال: 2021
ISSN: ['0343-6993', '1866-7414']
DOI: https://doi.org/10.1007/s00283-021-10058-w